On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation

In this study, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency and chaotic responses of the graphene nanoplatelets (GPLs)-reinforced composite (GPLRC) annular plate subject to an external harmonic load. Using Hamilton’s principle and the von Karman...

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Veröffentlicht in:	Engineering with computers Jg. 38; H. 3; S. 2583 - 2607
Hauptverfasser:	Ma, Lianghua, Liu, Xiaoliang, Moradi, Zohre
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	London Springer London 01.06.2022 Springer Nature B.V
Schlagworte:	Annular plates CAE) and Design Calculus of Variations and Optimal Control; Optimization Classical Mechanics Computer Science Computer-Aided Engineering (CAD Control Differential equations Dynamic models Dynamical systems Frequency response Generalized differential quadrature method Graphene Hamilton's principle Harmonic excitation Math. Applications in Chemistry Mathematical and Computational Engineering Nonlinear dynamics Original Article Perturbation Quadratures Systems Theory Thickness ratio GPLRC annular plate Quasi-harmonic motion Poincaré section Von Karman nonlinearity Chaotic responses
ISSN:	0177-0667, 1435-5663
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Abstract	In this study, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency and chaotic responses of the graphene nanoplatelets (GPLs)-reinforced composite (GPLRC) annular plate subject to an external harmonic load. Using Hamilton’s principle and the von Karman nonlinear theory, the nonlinear governing equation is derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. Various geometrically parameters are taken into account to investigate the chaotic motion of the annular plate subject to a harmonic excitation. The fundamental and golden results of this paper could be that the chaotic motion and nonlinear frequency of the annular plate are hardly dependent on the value of the length to thickness ratio ( l GPL / w GPL ) of the GPLs. Moreover, utilizing GPLs in the shapes close to square ( l GPL / w GPL = 1) presents higher frequency of the annular plate. Also, increase in l GPL / t GPL indicates that using GPLs with lower thickness relative to its length provides better frequency response
AbstractList	In this study, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency and chaotic responses of the graphene nanoplatelets (GPLs)-reinforced composite (GPLRC) annular plate subject to an external harmonic load. Using Hamilton’s principle and the von Karman nonlinear theory, the nonlinear governing equation is derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. Various geometrically parameters are taken into account to investigate the chaotic motion of the annular plate subject to a harmonic excitation. The fundamental and golden results of this paper could be that the chaotic motion and nonlinear frequency of the annular plate are hardly dependent on the value of the length to thickness ratio ( l GPL / w GPL ) of the GPLs. Moreover, utilizing GPLs in the shapes close to square ( l GPL / w GPL = 1) presents higher frequency of the annular plate. Also, increase in l GPL / t GPL indicates that using GPLs with lower thickness relative to its length provides better frequency response In this study, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency and chaotic responses of the graphene nanoplatelets (GPLs)-reinforced composite (GPLRC) annular plate subject to an external harmonic load. Using Hamilton’s principle and the von Karman nonlinear theory, the nonlinear governing equation is derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. Various geometrically parameters are taken into account to investigate the chaotic motion of the annular plate subject to a harmonic excitation. The fundamental and golden results of this paper could be that the chaotic motion and nonlinear frequency of the annular plate are hardly dependent on the value of the length to thickness ratio (lGPL/wGPL) of the GPLs. Moreover, utilizing GPLs in the shapes close to square (lGPL/wGPL = 1) presents higher frequency of the annular plate. Also, increase in lGPL/tGPL indicates that using GPLs with lower thickness relative to its length provides better frequency response
Author	Ma, Lianghua Liu, Xiaoliang Moradi, Zohre
Author_xml	– sequence: 1 givenname: Lianghua surname: Ma fullname: Ma, Lianghua organization: Weifang University of Science and Technology School of Mechanical Engineering – sequence: 2 givenname: Xiaoliang surname: Liu fullname: Liu, Xiaoliang email: lhymlh@126.com organization: Weifang University of Science and Technology School of Sergeancy – sequence: 3 givenname: Zohre surname: Moradi fullname: Moradi, Zohre email: z.moradi@edu.ikiu.ac.ir organization: Faculty of Engineering and Technology, Department of Electrical Engineering, Imam Khomeini International University
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Keywords	GPLRC annular plate Quasi-harmonic motion Poincaré section Von Karman nonlinearity Chaotic responses
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SubjectTerms	Annular plates CAE) and Design Calculus of Variations and Optimal Control; Optimization Classical Mechanics Computer Science Computer-Aided Engineering (CAD Control Differential equations Dynamic models Dynamical systems Frequency response Generalized differential quadrature method Graphene Hamilton's principle Harmonic excitation Math. Applications in Chemistry Mathematical and Computational Engineering Nonlinear dynamics Original Article Perturbation Quadratures Systems Theory Thickness ratio
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Title	On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation
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